President Uhuru Kenyatta was given the approval to go ahead and build 7,000 houses.
The decision was arrived at on Thursday following a refusal by the High Court to have the plan suspended pending an appeal.
Judge Wilfrida Okwany ruled that the connection between the civil servants, who filed the case, and the government is that of a landlord a tenant.
Additionally, the judge stated that the tenant could not prevent a landlord from taking over his house and carrying out development work as long as the lessee was given satisfactory notice to vacate the premises.
The judge further noted that the civil servants failed to prove that they were not able to secure alternative accommodation for themselves.
According to the judge, it was not enough for the tenants to merely state that they have school going children and disabled ones in the premises.
The public servants wanted the government to provide them with alternative accommodation before wrecking the houses.
During the hearing, the government argued that it had since 2014 planned to extend affordable housing to its citizens with full involvement of the applicants in line with the constitution.